Material models are useful for a wide variety of applications. As an example, product developers may use material models in their development efforts to fine tune equipment design. By way of particular example, designers of earth moving equipment may use models that simulate movement of the earth moving equipment as it operates on the soil. This particular type of modeling may be useful, for instance, to predict resistive forces experienced by the equipment.
One class of material models are so-called real time models such as virtually reality (VR) based models. These models have important potential applications in engineering. Included among these engineering applications are VR simulators with realistic force feedback for applications such as equipment design, equipment operator training, and the like. Referring again to an exemplary earthmoving equipment application, VR models may be useful for testing crashworthiness, operator training, and crashworthiness.
To date, however, these applications have had difficulties in achieving realistic and real-time modeling of the medium-tool interaction. Existing real-time models of the medium, such as granular soils, focus on creating visually pleasing graphics in virtual environments. In order to achieve real time speed, however, these models have sacrificed a detailed mechanics analysis of the soil. They are also limited in their ability to accurately estimate the force feedback exerted by the soil medium on the equipment and the vehicle engine.
Current real time material models such as soil models have other limitations. A majority of existing soil models are aimed at describing the deformation of the soil masses. The soil masses in these problems are typically modeled as continua. The preferred approach in analyzing these problems is to use quasi-static or dynamic nonlinear finite element analysis. Although they may look visually realistic, current continuum-based approaches to model real-time soil response have fundamental limitations that hamper their practical application.
For example, the change in particle position in a continuum model may be physically unrealistic. During a slope cut, for instance, a continuum model may move a soil particle at the top of the slope to the bottom of the re-equilibrated soil pile. This is not an accurate representation of reality, where a deep-seated slope failure and drastically different soil displacements are expected. If modeling a vehicle interaction with the soil, the force feedback into the vehicle dynamics is not based on realistic forces from the soil pile. Accordingly, continuum models of the soil are not capable of describing the large movement of the soil masses that occur in earthmoving operations.
The movements of masses of particulate material in response to manipulations by earth moving tools, such as loader buckets and bulldozer blades, follow very complex rules. Contrary to many existing real-time soil models, these rules are not local and often have global characteristics. Accurate modeling requires capturing the soil response due to large movement of soil particles caused by the equipment such as loading and dumping, digging and scraping. Soil masses may undergo significant changes in their geometry, including the formation and modification of the soil piles and the instability and failure of the slope in the existing soil pile.
Accurate discrete element models have been developed to describe the large movement of particulate and bulk materials. These models have been used in industrial material handling and mining applications. Discrete element models have also been used in modeling of the large movement of the soil and rock masses. The models simulate the individual particles and the interaction of each particle with particles surrounding and in contact with it. The discrete element method, by way of example, has been successfully used to model the flow of granular materials. Particles of granular material have been represented as simple geometric shapes, such as circular, elliptic or polygonal discs in two-dimensional models and equivalent shapes in three-dimensional models. Because discrete element soil models may accurately simulate the response of the soil mass to earthmoving equipment, they may seem an appropriate choice for VR applications. However, a major drawback of the discrete element models in VR applications is very long computer run times.
Reasonably small discrete element problems with less than 1000 particles may require run times of anywhere from several hours to several days on a typical computer workstation. Realistic models of soil mass on in typical VR applications would require in excess of a hundred thousand three-dimensional particles. Computer simulation of such large systems for several minutes of real time would require several days of CPU time on even the fastest super-computers.
These and other problems remain unresolved in the art.